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88
Basket Default Swaps, CDO's and Factor Copulas
 JOURNAL OF RISK
, 2003
"... We consider a factor approach to the pricing of basket credit derivatives and synthetic CDO tranches. Our purpose is to deal in a convenient way with dependent defaults for a large number of names. We provide semiexplicit expressions of the stochastic intensities of default times and pricing formul ..."
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Cited by 121 (7 self)
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We consider a factor approach to the pricing of basket credit derivatives and synthetic CDO tranches. Our purpose is to deal in a convenient way with dependent defaults for a large number of names. We provide semiexplicit expressions of the stochastic intensities of default times and pricing formulae for basket default swaps and CDO tranches. Two cases are studied in detail: meanvariance mixture models and frailty models. We also compare prices under Gaussian and Clayton copulas.
Contagion in financial networks
 Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
"... This paper develops an analytical model of contagion in financial networks with arbitrary structure. We explore how the probability and potential impact of contagion is influenced by aggregate and idiosyncratic shocks, changes in network structure, and asset market liquidity. Our findings suggest th ..."
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Cited by 95 (1 self)
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This paper develops an analytical model of contagion in financial networks with arbitrary structure. We explore how the probability and potential impact of contagion is influenced by aggregate and idiosyncratic shocks, changes in network structure, and asset market liquidity. Our findings suggest that financial systems exhibit a robustyetfragile tendency: while the probability of contagion may be low, the effects can be extremely widespread when problems occur. And we suggest why the resilience of the system in withstanding fairly large shocks prior to 2007 should not have been taken as a reliable guide to its future robustness.
Common failings: how corporate defaults are correlated
 Journal of Finance
, 2007
"... We test the doubly stochastic assumption under which firms ’ default times are correlated only as implied by the correlation of factors determining their default intensities. Using data on U.S. corporations from 1979 to 2004, this assumption is violated in the presence of contagion or “frailty ” (un ..."
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Cited by 83 (4 self)
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We test the doubly stochastic assumption under which firms ’ default times are correlated only as implied by the correlation of factors determining their default intensities. Using data on U.S. corporations from 1979 to 2004, this assumption is violated in the presence of contagion or “frailty ” (unobservable explanatory variables that are correlated across firms). Our tests do not depend on the timeseries properties of default intensities. The data do not support the joint hypothesis of wellspecified default intensities and the doubly stochastic assumption. We find some evidence of default clustering exceeding that implied by the doubly stochastic model with the given intensities. WHY DO CORPORATE DEFAULTS CLUSTER IN TIME? Several explanations have been explored. First, firms may be exposed to common or correlated risk factors whose comovements cause correlated changes in conditional default probabilities. Second, the event of default by one firm may be “contagious, ” in that one such event may directly induce other corporate failures, as with the collapse of Penn
Is credit event risk priced? Modeling contagion via the updating of beliefs
, 2003
"... We propose a reducedform model where jumpstodefault are priced because they generate a marketwide jump in credit spreads. While this framework is consistent with a counterparty risk interpretation (e.g., Jarrow and Yu (2001)), it is most naturally interpreted as an updating of beliefs due to an ..."
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Cited by 73 (5 self)
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We propose a reducedform model where jumpstodefault are priced because they generate a marketwide jump in credit spreads. While this framework is consistent with a counterparty risk interpretation (e.g., Jarrow and Yu (2001)), it is most naturally interpreted as an updating of beliefs due to an unexpected event. Simple analytic solutions are obtained for the prices of risky debt regardless of the number of firms that share in the contagious response. As a special case, we show that the contagious response can be induced via a liquidityshock, with no impact on actual default intensities. Empirically, we find that credit events of large firms generate a market wide increase in credit spreads and a significant ‘flighttoquality ’ response in the Treasury market. A calibration argument suggests that the premium associated with jumptodefault risk for a typical investment grade firm has an upper bound of a few basis points per year, but that the risk premium for contagionrisk may be considerably larger.
Frailty Correlated Default
, 2008
"... This paper shows that the probability of extreme default losses on portfolios of U.S. corporate debt is much greater than would be estimated under the standard assumption that default correlation arises only from exposure to observable risk factors. At the high confidence levels at which bank loan p ..."
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Cited by 68 (4 self)
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This paper shows that the probability of extreme default losses on portfolios of U.S. corporate debt is much greater than would be estimated under the standard assumption that default correlation arises only from exposure to observable risk factors. At the high confidence levels at which bank loan portfolio and CDO default losses are typically measured for economiccapital and rating purposes, our empirical results indicate that conventionally based estimates are downward biased by a full order of magnitude on test portfolios. Our estimates are based on U.S. public nonfinancial firms existing between 1979 and 2004. We find strong evidence for the presence of common latent factors, even when controlling for observable factors that provide the most accurate available model of firmbyfirm default probabilities. ∗ We are grateful for financial support from Moody’s Corporation and Morgan Stanley, and for research assistance from Sabri Oncu and Vineet Bhagwat. We are also grateful for remarks from Torben Andersen, André Lucas, Richard Cantor, Stav Gaon, Tyler Shumway, and especially Michael Johannes. This revision is much improved because of suggestions by a referee, an associate editor, and Campbell Harvey. We are thankful to Moodys and to Ed Altman for generous assistance with data. Duffie is at The Graduate School of Business, Stanford University. Eckner and Horel are at Merrill Lynch. Saita is at Lehman
Credit risk modeling and valuation: an introduction
 In D. Shimko. Credit Risk: Models and Management
, 2004
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Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk
, 2005
"... We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of e ..."
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Cited by 34 (6 self)
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We propose a twosided jump model for credit risk by extending the LelandToft endogenous default model based on the geometric Brownian motion. The model shows that jump risk and endogenous default can have significant impacts on credit spreads, optimal capital structure, and implied volatility of equity options: (1) The jump and endogenous default can produce a variety of nonzero credit spreads, including upward, humped, and downward shapes; interesting enough, the model can even produce, consistent with empirical findings, upward credit spreads for speculative grade bonds. (2) The jump risk leads to much lower optimal debt/equity ratio; in fact, with jump risk, highly risky firms tend to have very little debt. (3) The twosided jumps lead to a variety of shapes for the implied volatility of equity options, even for long maturity options; and although in generel credit spreads and implied volatility tend to move in the same direction under exogenous default models, but this may not be true in presence of endogenous default and jumps. In terms of mathematical contribution, we give a proof of a version of the “smooth fitting ” principle for the jump model, justifying a conjecture first suggested by Leland and Toft under the Brownian model. 1
CopulaBased models for financial time series
, 2007
"... This paper presents an overview of the literature on applications of copulas in the modelling of financial time series. Copulas have been used both in multivariate time series analysis, where they are used to charaterise the (conditional) crosssectional dependence between individual time series, ..."
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Cited by 33 (0 self)
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This paper presents an overview of the literature on applications of copulas in the modelling of financial time series. Copulas have been used both in multivariate time series analysis, where they are used to charaterise the (conditional) crosssectional dependence between individual time series, and in univariate time series analysis, where they are used to characterise the dependence between a sequence of observations of a scalar time series process. The paper includes a broad, brief, review of the many applications of copulas in finance and economics.